MHB Solving an exponential equation

[Sharpy1]

I'm doing some optional problems in preparation for my final in two weeks in one of my classes and I'm stumped on this one in particular

Express irrational solutions in exact form and as a decimal rounded to three decimal places.

Problem: 0.3(4^0.2x) = 0.2

I won't be able to look back here for a few days so some help within the next hour or so would be nice but not required thanks in advance for the help!

 

[MarkFL]

Re: Logarithmic Function Help Plz :(

I would begin by expressing the equation as follows:

$$4^{\frac{x}{5}}=\frac{2}{3}$$

Now, given:

$$a^b=c$$

this implies:

$$\log_a(c)=b$$

So, how can you convert the above equation from exponential to logarithmic form?